document.write( "Question 718048: if a man and a boy can do a work in 8 days,this work can do 2 man and 4 boy in 3 days .how many days it will takes if a man or a boy do alone? \n" ); document.write( "
Algebra.Com's Answer #440733 by josmiceli(19441)\"\" \"About 
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Let \"+r%5B1%5D+\" = the rate that the man works
\n" ); document.write( "Let \"+r%5B2%5D+\" = the rate that the boy works
\n" ); document.write( "Add their rates to get rate working together
\n" ); document.write( "( 1 job ) / ( 8 days ) is rate working together, so
\n" ); document.write( "(1) \"+r%5B1%5D+%2B+r%5B2%5D+=+1%2F8+\"
\n" ); document.write( "-----------------------------
\n" ); document.write( "Then you are given the case with 2 times the rate for a man
\n" ); document.write( "and 4 times the rate for a boy
\n" ); document.write( "(2) \"+2r%5B1%5D+%2B+4r%5B2%5D+=+1%2F3+\"
\n" ); document.write( "-------------------------------
\n" ); document.write( "Multiply both sides of (1) by \"+2+\"
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) \"+2r%5B1%5D+%2B+4r%5B2%5D+=+1%2F3+\"
\n" ); document.write( "(1) \"+-2r%5B1%5D+-+2r%5B2%5D+=+-2%2F8+\"
\n" ); document.write( "\"+2r%5B2%5D+=+1%2F3+-+1%2F4+\"
\n" ); document.write( "\"+2r%5B2%5D+=+4%2F12+-+3%2F12+\"
\n" ); document.write( "\"+2r%5B2%5D+=+1%2F12+\"
\n" ); document.write( "\"+r%5B2%5D+=+1%2F24+\"
\n" ); document.write( "and, since
\n" ); document.write( "(1) \"+r%5B1%5D+%2B+r%5B2%5D+=+1%2F8+\"
\n" ); document.write( "(1) \"+r%5B1%5D+%2B+1%2F24+=+1%2F8+\"
\n" ); document.write( "(1) \"+r%5B1%5D+%2B+1%2F24+=+3%2F24+\"
\n" ); document.write( "(1) \"+r%5B1%5D+=+2%2F24+\"
\n" ); document.write( "(1) \"+r%5B1%5D+=+1%2F12+\"
\n" ); document.write( "------------------------
\n" ); document.write( "A man, working alone can do 1 job in 12 days
\n" ); document.write( "A boy, working alone, can do 1 job in 24 days
\n" ); document.write( "-----------------
\n" ); document.write( "check the answer:
\n" ); document.write( "(2) \"+2r%5B1%5D+%2B+4r%5B2%5D+=+1%2F3+\"
\n" ); document.write( "(2) \"+2%2A%281%2F12%29+%2B+4%2A%281%2F24%29+=+1%2F3+\"
\n" ); document.write( "(2) \"+1%2F6+%2B+1%2F6+=+1%2F3+\"
\n" ); document.write( "(2) \"+1%2F6+%2B+1%2F6+=+2%2F6+\"
\n" ); document.write( "OK\r
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